Why is the winner's payment divided equally among the other applicants for a domain?

This is the simplest and fairest way to do this. Others have suggested dividing it proportionally to each bidder's highest bid - but we have found that encourages gaming and causes prices to be higher for the auction winner, thus biasing the system against the winners.

Why will winners have to pay less in the Applicant Auction than in the Last Resort Auction?

There are many ways to explain this - here is a quick summary of the general idea:
In the Applicant Auction, you get paid if you don't win. In the Last Resort Auction, you get nothing if you don't win. Therefore losing is worse in the Last Resort auction, and bidders will try to avoid it harder. How do you avoid losing? You bid more. What happens if people bid more? The winner pays more.

What happens if someone wins in the auction and doesn't pay?

In this case, they forfeit their 20% deposit and have their application withdrawn, in addition to facing further legal action. In light of this, we think it's extremely unlikely that this will happen.

How much will this cost?

Winners do not need to pay a commission on the winning price. A modest compensation for running the auction is taken out of the payments that are distributed to sellers. The fee for the market facilitator is 4%, which covers the cost of services from Deloitte and the escrow agent.